Solitary Wave Solutions of Some Conformable Time-Fractional Coupled Systems via an Analytic Approach

Abstract

The main purpose of this research is to inquire the new solitary wave solution of the coupled time-fractional models to validate the influence and proficiency of the planned variational iteration method (VIM) using conformable derivative definition. Applications to four demanding nonlinear problems like Hirota-Satsuma coupled KdV equations, modified Boussinesq (MB) equation, approximate long wave (ALW) equation and Drinfeld-Sokolov-Wilson (DSW) equation demonstrate the efficiency and the robustness of the method. An analysis of the consequences with effects of relevant parameters and comparison with the exact solution presented with the help of graphs tables and gives the further understanding of numerical results by others. The convergence of the method is illustrated numerical and their physical significance is discussed

Computational Solution of Fractional Reaction Diffusion Equations via an Analytical Method

“…Consider the solution in fractional Taylor series (10) The recurrence relation for non-linear source term is (11) where represents Adomian polynomial defined by (6) Thus, the required solution is obtained by (12)…”

“…Linear and non-linear FODEs have been solved using different methods in this regard. In [9], for example, has a discussion of the modified Bernoulli sub-equation and non-linear time fractional Burgers equations. In [10,11] was carried out a computational simulation of space fractional diffusion equations.…”

“…In [10,11] was carried out a computational simulation of space fractional diffusion equations. The four variants of time-fractional nonlinear Caputo-type Newell-Whitehead-Segel (NWS) problem are solved by fractional variational iteration method in [9]. The solution of Burgers-Huxley models [13] has been computed using OHAM.…”

Compaction in a Class of Nonlinear Partial Differential Equations

“…Various effort follows in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] to learn the profound subjective alteration during really nonlinear marvel brought about by the simply nonlinear dispersive model. Rosenau and Hyman [2]…”

“…In any case, Kivshar [9] anticipated the presence of split compaction, someplace he demonstrated that fracture with conservative help may exist in a cross-section of an equal particle using an incompatible coupling. Kivshar [9] examined the following models:…”